Ramachandran plot for Alanine Dipeptide

TO USE THE FUNCTION LIBRARY (VERSION UP TO DATE) IN THE INTERACTIVE SHELL:
you@eulerX ~$ module load courses mmm ; mmm-init

Alanine dipeptide is often studied in theoretical work because it is among the simplest systems to exhibit some of the important features common to biomolecules. It has more than one long-lived conformational state. The relevant angles are the dihedral angles of the backbone, commonly called Φ and Ψ (see figure). In the following scheme, light blue atoms are carbons, white ones are hydrogens, red are oxygens, and blue are nitrogens. So the torsional angle Φ is C-N-C-C and Ψ is N-C-C-N along the backbone.

A detailed study of this system (see 10.1073/pnas.100127697) shows the presence, in vacuum of two stable states:

The diagram represents the contour lines of the molecular energy as a function of the two dihedral angles. Contour lines are separated by 2 kcal/mol.

In this exercise you will obtain a simplified version of the above potential energy surface, obtained in a very similar way as in the paper. You will constrain the angles at fixed values using a strong harmonic potential, and optimize all other degrees of freedom. From this, a grid of energies will be built, and the energy diagram (Ramachandran plot) will be constructed.

The file “a1a2ene” will contain three columns: the two constrained dihedral angles, and the corresponding energy.
Using gnuplot, you can visualize the results

you@eulerX exercise_2.2$ gnuplot torsion.gnu

Changing into the directory Logs you fill find files of the kind opt.?.?.pdb . You can now verify that the target torsional angles have been reached. To this end you can either use the graphical program vmd (first, load the module with module load vmd) or the function
m_pdbtorsion: